The present invention relates to an image forming apparatus using a rod lens array. More particularly, the invention relates to an image forming apparatus which secures uniformity of resolution while retaining its fundamental resolving power by disposing an object surface and an image surface at appropriate positions. This technique is useful when it is applied to a contact image sensor or an LED printer.
As shown in FIG. 1, a rod lens array 10 is constructed as an unit magnification imaging optical system in which a number of rod lenses 12 each having a refractive index distribution in the radial direction are arrayed such that their optical axes are arranged parallel to one another. The unit magnification imaging optical system is widely employed in facsimile equipment, copying machines, scanners, LED printers and the like. An object surface 14 is disposed facing one end faces of the rod lenses 12, and an image surface 16 is disposed facing the other end faces thereof. In an image reading system, such as a contact image sensor shown in FIG. 2, the object surface 14 is an original document surface and the image surface 16 is a sensor pixel contained surface. In an image writing system, such as an LED printer, the object surface is a light emitting surface of the LED elements, and the image surface is a drum surface.
In designing an optical position relationship in those image forming apparatuses, it is essential to set an average value MTFave of the MTF (modulation transfer function) at the largest possible value. The average value MTFave is an average value of the MTF as calculated in the lens array direction (=longitudinal direction of the rod lens array). Incidentally, the MTF indicates a fundamental resolving power of the rod lens array. To this end, the object surface 14 and the image surface 16 are positioned so as to satisfy at least the following condition: a lens working distance Lo on the object side (=distance from one lens end face to the object surface) is optically equal to a lens working distance Lo on the image side (=distance from the other lens end face to the image surface). Another approach, sometimes employed, is to adjust a distance TC between the object surface and the image surface (referred to as an object-image distance TC) so as to maximize the average value MTFave of the MTF.
The MTF is given by the following equation:
MTF(%)=[(imaxxe2x88x92imin)/(imax+imin)]xc3x97100 
In the above equation, the terms imax and imin are obtained in the following manner. As shown in FIG. 3, a rod lens array 10 receives a rectangular grating pattern (=original image) 20, and forms an image 22 of the pattern. A sensor receives the image 22. The relative maximum imax and the relative minimum imin of a light amount of the received image 22 are measured. It is evaluated that as the MTF is closer to 100%, an image formed by the optical system more accurately resembles an original image (the resolving power of the optical system is larger).
The actual measurement is conducted using an optical system as shown in FIG. 4. In the figure, light emitted from a light source 30 such as a halogen lamp passes through a filter 31, a diffusion plate 32, and a rectangular test chart 33. As a result, a rectangular grating pattern is formed. The rod lens array 10 forms an image of the rectangular grating pattern. A CCD image sensor 34 receives the image and transforms it into a corresponding electrical signal. The rod lens array 10 is moved in the direction of a void arrow. Through the movement of the rod lens array, the image is inspected over the entire length thereof. A waveform of an output signal of the CCD image sensor 34 is output to a data processor 35. The data processor 35 appropriately processes the output waveform to have the relative maximum imax and the relative minimum imin of the waveform, and computes the MTF by using them. An average value of the MTF as computed in the lens array direction is the MTFave of the lens array.
In addition to the approach to adjust the object-image distance TC so as to maximize the average value MTFave of the MTF, there is another approach. For example, in an image reading system, if the presence of a platen glass can restrict a position deviation of an original document in only one direction, an optimum focus position on the object surface side is offset away from the platen glass surface, in order to increase an apparent focal depth. This approach is so-called a one-side offset arrangement. In yet another approach, an image writing system can employ a defocused positional relationship in order to lessen the adverse influence of the variations in the light emissions of the LED elements.
In the rod lens, the resolution is distributed in the radial direction within a visual field. Consequently, an image superimposed by the rod lens array contains the resolution fluctuation in the longitudinal direction at a cycle of the lens radius (when the sensor pixel/LED element is aligned with the center position of the lens array) or at a cycle of the lens diameter (when the sensor pixel/LED element is not aligned with the center position of the lens array). If the rod lens array currently marketed is used at the resolution power of 600 dip or higher, this resolution fluctuation is not negligible.
Recent higher resolution tendency of applications causes a fact that the conventional technique cannot secure uniformity of the resolution while retaining its fundamental resolving power. In handling the half-tone image used in the image reading/writing system, the optical density non-uniformity frequently occurs.
Accordingly, an object of the present invention is to provide an image forming apparatus which secures uniformity of resolution in the lens array direction, while retaining the fundamental resolving power, and hence lessens the optical density non-uniformity to be negligible even in handling the half-tone image.
According to the present invention, there is provided an image forming apparatus which uses an unit magnification imaging rod lens array including a number of rod lenses each having a refractive index distribution in the radial direction and being arrayed such that their optical axes are arranged parallel to one another, and in which an object surface is disposed facing one end face of a rod lens array, while an image surface is disposed facing the other end face thereof, and a lens working distance of the rod lens array on the object side is substantially equal to that on the image side. The image forming apparatus is improved such that an actual object-image distance Tco is set between the conjugate length TC1 at which the average value MTFave of the MTF of the rod lens array in the lens array direction is maximized and the conjugate length TC2 at which the xcex94MTF(=(MTFmaxxe2x88x92MTFmin)/MTFave) is minimized, or the actual object-image distance Tco is equal to the conjugate length TC2 at which the xcex94MTF is minimized and a shift quantity xcex94TC(=|TCoxe2x88x92TC1|) is set within 0 mm less than xcex94TC less than +0.2 mm with respect to the conjugate length TC1 at which the MTFave is maximized. In the image forming apparatus, it is more preferable that the object-image distance Tco is set within +0.05 mm less than xcex94TC less than +0.15 mm.
The inventors of the present patent application studied such a phenomenon that when the half-tone image is used at high resolution, the optical density non-uniformity is noticeable, and reached the following conclusion. Through the study, the following facts were found: 1) It is convenient to use a new parameter xcex94MTF in evaluating the optical density non-uniformity, and 2) Generally, a conjugate length TC1 at which the average value MTFave of the MTF in the lens array direction (longitudinal direction) is maximized is not equal to a conjugate length TC2 at which xcex94MTF is minimized.
As described above, in the invention, the actual object-image distance Tco is set between the conjugate length TC1 at which the average value MTFave of the MTF of the rod lens array in the lens array direction is maximized and the conjugate length TC2 at which the xcex94MTF(=(MTFmaxxe2x88x92MTFmin)/MTFave) is minimized, or the actual object-image distance Tco is equal to the conjugate length TC2 at which the xcex94MTF is minimized and a shift quantity xcex94TC(=|TCoxe2x88x92TC1|) is set within 0 mm less than xcex94TC less than +0.2 mm with respect to the conjugate length TC1 at which the MTFave is maximized. A direction in which the conjugate length TC2 at which xcex94MTF is minimized is shifted with respect to the conjugate length TC1 at which the MTFave is maximized, is determined by a refractive index distribution coefficient of the rod lens and the like (the direction: + direction in which the conjugate length increases or xe2x88x92 direction in which it decreases). Accordingly, in the invention, it is important that the actual object-image distance Tco is set between the conjugate length TC1 at which the average value MTFave of the MTF of the rod lens array in the lens array direction is maximized and the conjugate length TC2 at which the xcex94MTF is minimized. Further, in the invention, the lens working distance of the rod lens array on the object side is substantially equal to that on the image side. Accordingly, an optical shift quantity on each of the object side and the image side is xcex94TC/2. Because of this, the decrease of the average value MTFave of the MTF is within a tolerable range. The uniformity of resolution in the lens array direction is secured while sustaining the high resolving power. Accordingly, the optical density non-uniformity is negligible even in handling the half-tone image.
The present disclosure relates to the subject matter contained in Japanese patent application No. 2000-207380 (filed on Jul. 7, 2000), which is expressly incorporated herein by reference in its entirety.